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342                               CHEMICAL ENGINEERING
action from the surface of the solid. It is assumed, that we have at all times direct contact with the solid particles during the process of dissolution a thin fi of saturated solution, and that the unsaturated solution never has contact wi the solid but becomes concentrated by diffusion from this film.
It then becomes evident that the actual velocity of dissolution may be qu different from the observed velocity, due to the rate of this diffusion.    There is need to consider these two velocities separately except to explain some exceptioi phenomena* discussed later under the laws of mass action.
The velocity of diffusion is dependent upon the osmotic pressure exerted by 1 material in solution. If some copper-sulphate crystals are placed in the bottom o jar of water they will dissolve and a layer of dark-blue solution will form in the bott< around the crystals which will diffuse up through the rest of the solution very slov until it is all of the same concentration. It required a perfectly definite force to this heavier material up through this solution and this force was osmotic pressu Therefore, more highly ionized solutes should diffuse through the solvent irn rapidly than slightly ionized materials as the osmotic pressure exerted by the lat is less than the former. The second, third and fourth factors listed above as affect i the speed of the dissolution arc related together by^the law of mass action follow! 3
Law of Mass Action.  Since dissolution of a solid in liquid is a chemi reaction it must be governed by the simple laws of mass action and therefore i1 possible to develop an expression concerning the velocity of this reactii Ostwald, Brunner and others have done a certain amount of work on this subj< and the following discussion is derived largely from their work.
The speed of dissolution is directly dependent upon the amount of surface expo* to the action of the solvent and upon the concentration of the solute in the solve  Therefore, if we let
S = surface,
x  the concentration of the solution at any time,
a = the concentration of the film of saturated solution in direct contact with i solid,
t = time,                                                         dx  very small change of x,
K = constant  dependent upon solvent,            dt  very small interval of tint
we may obtain the following expression :
By integrating this expression we obtain l/tloge a/a -x = KS
This formula will only hold true if S remains constant. But it has been found many cases that though the surface exposed did change materially, still the rale dissolution KS remained constant. This would seem therefore to show that I second step (velocity of diffusion) here were controlling the action. In other woi the diffusion of the solid from the saturated film to the solution itself was so slow i I the surface exposed was more than enough to resaturate the film with solid a.s diffused to the rest of the solution, and this fact supports the assumption made earl in the paper that the process of dissolution is made in these two steps.
Returning to the formula above (No. 2) it will be seen that the value of x (that the concentration of the solid in the solution) varies with time according to t logarithmic curve, Fig. 1. We would naturally suppose that the speed of dissoluii would decrease as the solvent becomes more saturated with the solute but it in interest to note the curve that relates to these two factors.